Behavior of Soft Spheres During Impact by High-Speed Photography

Abstract

Previously, it has been verified experimentally for durations of impact that the Hertz theory (the quasi-statical theory) holds during impact of spheres without any exception. However, no measurement of duration of impact has been presented for spheres of materials other than metal. This study presents exceptional cases of impacts of spheres during which the Hertz model does not directly hold. By the use of a high-speed camera running at a speed of 5000 frames/s, durations of impact are measured directly for impacts of two solid rubber spheres of the same size and content and impacts of a soft ball (Japanese type-soft tennis ball) on a rigid foundation. As a result, the measured durations of impact in the two impacting cases are found to be decreased as the impact velocity is increased, similar in tendency to durations of impact of elastic metal spheres during which the Hertz theory holds. However, the measured durations of impact are found to be clearly shorter than results calculated according to the Hertz theory, approximately half in the former impacts at high impact velocities, and about 70 percent of the Hertzian results in the latter impacts at almost all impact velocities. Deformation process of the ball impacting on the foundation is also presented to indicate both durations in the compressive process and the restitution one to be shorter than those expected by the Hertz theory. The other results observed on the films are noted to investigate the origin of the great discrepancies between the measured and Hertzian durations (that is, the impacting mechanism of the rubber spheres or the rubber ball packed with air treated here).